\subsection{BCS}
\subsubsection{Classic BCS Paper}

\begin{description}
 \item [\cite{BogoliubovColl}] First one get Anderson-Bogoliubov mode in BCS.  (Eq. (4.16))  It also states that non-zero central momentum components are necessary for collective mode(sec. 4.2).  It linearized the Fr\"{o}hlich Hamiltonian with non-zero expectation of the normal expectation as well as abnormal ones (keep the non-zero central momentum quantities). 
  \item [\cite{AndersonBCS}]Get bosonic mode, Anderson-Bogoliubov mode, in BCS with  equation of motion method.  One has to introduce none-zero central momentum interaction to reduced BCS hamiltonian to get it.  The linearization is specific for BCS ansatz, i.e., non-zero mean-field value for anonymous pair expectation. In the final result for excitation, the excitation also expanded around only zero-central-momentum and others are approximated by zero-central-momentum quantities, i.e., BCS ground state value. 
   
   $\bar{A}$ is the time reversal of $A$ (opposite momentum and opposite spin).
	 
\item[\cite{Rickayzen}] Use the same equation of motion method as \cite{AndersonBCS}, but with a canonical transformation first.  So the resulting equation is much simpler. 
\item[\cite{BcsExact}] with useful citations to others.        
 \end{description}

\subsection{Collective Mode}
\begin{description}
\item[\cite{RanderiaBEC, Randeria1997,Randeria2008}]Summary of path integral approach for single-channel crossover problem.  It got mean-field as well as the Gaussian correction, which leads to collective modes.   
\end{description}

\subsection{Feshbach Resonance}
\subsubsection{Basics}
\subsubsection{Narrow}
\begin{description}
  \item [\cite{JacksonNarrow}]Nice study with two-channel model and how to renormalize it. 
	
 \end{description}
 
\subsection{Miscellaneous}
\subsection{}
\begin{description}
\item[\cite{Politzer}]He discuss the difference of BEC fluctuation between in canonical ensemble and in grand-canonical ensemble.  In grand-canonical ensemble that the fluctuation of ground-state can be as large as $N$.  However, in canonical ensemble, the fluctuation of ground state is equal to that of all excited state and stays finite all the time.  But other quantities seem to be fine between two framework.  
\item[\cite{Tan2008-1,Tan2008-2}]Tan basically match the wave function to the Betha-Pierels boundary condition/ $1/r-1/a$ (s-wave scattering) boundary condition.  (His $\eta(r)$ function).  He divide the phase space into two parts:  the free (long-range) part ($D(\epsilon)$) and the short-range (non-free) part ($I(\epsilon)$).  He proved that the quantity he studied (such as internal energy) has negligible weight in $I(\epsilon)$, and in $D(\epsilon)$, we simply need to count all the kinetic energy there because it is free part without any interaction.  
Questions:\\
* Why the kinetic energy in $D(\epsilon)$ goes as $C$ which relates to the high-momentum ?\\
* What happens for $I(\epsilon)$ has more weight?
\end{description}

\subsection{Books}
\begin{description}
\item[\cite{Altland}]A very nice introduction of path integral method in condensed matter context.  A good description of Hubbard-Stratonovich transformation, and its use in superconductivity.  It even mentions BCS-BEC crossover in one of its problems. 
\end{description}